Mathematical Foundations and Applications of Graph Entropy

Matthias Dehmer , Frank Emmert-Streib , Zengqiang Chen , Xueliang Li , Yongtang Shi 지음

Wiley-VCH 2016년 07월 19일 출간

작품소개

책소개

This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.

목차

List of Contributors XI Preface XV 1 Entropy and Renormalization in Chaotic Visibility Graphs 1Bartolo Luque, Fernando Javier Ballesteros, Alberto Robledo, and Lucas Lacasa 1.1 Mapping Time Series to Networks 2 1.1.1 Natural and Horizontal Visibility Algorithms 4 1.1.2 A Brief Overview of Some Initial Applications 8 1.1.2.1 Seismicity 8 1.1.2.2 Hurricanes 8 1.1.2.3 Turbulence 9 1.1.2.4 Financial Applications 9 1.1.2.5 Physiology 9 1.2 Visibility Graphs and Entropy 10 1.2.1 Definitions of Entropy in Visibility Graphs 10 1.2.2 Pesin Theorem in Visibility Graphs 12 1.2.3 Graph Entropy Optimization and Critical Points 19 1.3 Renormalization Group Transformations of Horizontal Visibility Graphs 26 1.3.1 Tangent Bifurcation 29 1.3.2 Period-Doubling Accumulation Point 31 1.3.3 Quasi-Periodicity 32 1.3.4 Entropy Extrema and RG Transformation 34 1.3.4.1 Intermittency 35 1.3.4.2 Period Doubling 35 1.3.4.3 Quasi-periodicity 35 1.4 Summary 36 1.5 Acknowledgments 37 References 37 2 Generalized Entropies of Complex and Random Networks 41Vladimir Gudkov 2.1 Introduction 41 2.2 Generalized Entropies 42 2.3 Entropy of Networks: Definition and Properties 43 2.4 Application of Generalized Entropy for Network Analysis 45 2.5 Open Networks 53 2.6 Summary 59 References 60 3 Information Flow and Entropy Production on Bayesian Networks 63Sosuke Ito and Takahiro Sagawa 3.1 Introduction 63 3.1.1 Background 63 3.1.2 Basic Ideas of Information Thermodynamics 64 3.1.3 Outline of this Chapter 65 3.2 Brief Review of Information Contents 66 3.2.1 Shannon Entropy 66 3.2.2 Relative Entropy 67 3.2.3 Mutual Information 68 3.2.4 Transfer Entropy 69

작가정보

저자(글) Matthias Dehmer

Matthias Dehmer studied mathematics at the University of Siegen (Germany) and received his Ph.D. in computer science from the Technical University of Darmstadt (Germany). Afterwards, he was a research fellow at Vienna Bio Center (Austria), Vienna University of Technology, and University of Coimbra (Portugal). He obtained his habilitation in applied discrete mathematics from the Vienna University of Technology. Currently, he is Professor at UMIT - The Health and Life Sciences University (Austria) and also holds a position at the Universit t der Bundeswehr M nchen. His research interests are in applied mathematics, bioinformatics, systems biology, graph theory, complexity and information theory. He has written over 180 publications in his research areas. Frank Emmert-Streib studied physics at the University of Siegen (Germany) gaining his PhD in theoretical physics from the University of Bremen (Germany). He received postdoctoral training from the Stowers Institute for Medical Re- search (Kansas City, USA) and the University of Washington (Seattle, USA). Currently, he is an associate professor at the Queen's University Belfast (UK) at the Center for Cancer Research and Cell Biology heading the Computational Biology and Machine Learning Laboratory. His main research interests are in the field of computational medicine, network biology and statistical genomics.

저자(글) Frank Emmert-Streib

저자(글) Zengqiang Chen

저자(글) Xueliang Li

저자(글) Yongtang Shi